6.6.2.5 Exact and Inexact Numbers

R5RS requires that, with few exceptions, a calculation involving inexact
numbers always produces an inexact result. To meet this requirement,
Guile distinguishes between an exact integer value such as ‘5’ and
the corresponding inexact integer value which, to the limited precision
available, has no fractional part, and is printed as ‘5.0’. Guile
will only convert the latter value to the former when forced to do so by
an invocation of the inexact->exact procedure.

The only exception to the above requirement is when the values of the
inexact numbers do not affect the result. For example (expt n 0)
is ‘1’ for any value of n, therefore (expt 5.0 0) is
permitted to return an exact ‘1’.

Scheme Procedure: exact?z

C Function: scm_exact_p(z)

Return #t if the number z is exact, #f
otherwise.

(exact? 2)
⇒ #t
(exact? 0.5)
⇒ #f
(exact? (/ 2))
⇒ #t

C Function: intscm_is_exact(SCM z)

Return a 1 if the number z is exact, and 0
otherwise. This is equivalent to scm_is_true (scm_exact_p (z)).

An alternate approch to testing the exactness of a number is to
use scm_is_signed_integer or scm_is_unsigned_integer.

Scheme Procedure: inexact?z

C Function: scm_inexact_p(z)

Return #t if the number z is inexact, #f
else.

C Function: intscm_is_inexact(SCM z)

Return a 1 if the number z is inexact, and 0
otherwise. This is equivalent to scm_is_true (scm_inexact_p (z)).

Scheme Procedure: inexact->exactz

C Function: scm_inexact_to_exact(z)

Return an exact number that is numerically closest to z, when
there is one. For inexact rationals, Guile returns the exact rational
that is numerically equal to the inexact rational. Inexact complex
numbers with a non-zero imaginary part can not be made exact.

(inexact->exact 0.5)
⇒ 1/2

The following happens because 12/10 is not exactly representable as a
double (on most platforms). However, when reading a decimal
number that has been marked exact with the “#e” prefix, Guile is
able to represent it correctly.